Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
486 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22627119 | C2 | semidirect |
| 3. #22627007 | C2 | semidirect |
| 146. C4×C73 | #349 | semidirect |
| 149. Dic73 | #349 | semidirect |
| 165. C73 | #12785 | semidirect |
| 314. C4 | #17989686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627119 | 2 |
| C2×#17989686 | 2 |
| #22627007 | 2 |
| C2×C4×#11924038 | 2 |
| #12785 | 73 |